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针对边坡失效概率计算中功能函数难以确定、多重积分计算不便等问题,提出了Copula理论下基于g-line失效域的边坡可靠性分析方法。首先简要介绍了Copula理论,给出了基于Copula理论的边坡可靠性分析步骤,进而探讨了一般均质边坡的g-line曲线拟合形状及表征边坡失效域的抗剪强度参数范围,结果表明,二次多项式能很好拟合g-line曲线,内摩擦角和黏聚力可表征g-line曲线下的边坡失效域。以一均质边坡为例,通过在g-line失效域内积分,得出了3种Copula函数下边坡的失效概率,均与FORM及MCS法得出的结果比较接近,从而验证了Copula理论下基于g-line失效域的边坡可靠性分析方法的合理性。最后,讨论了不同Copula函数下失效概率计算结果的差异性随安全系数变化的特点,认为在低失效概率(高安全系数)时,可靠性分析结果对Copula函数类型比较敏感,应重视不同Copula函数类型引起的计算结果差异性及最优化问题的研究。
In view of the difficulty in determining the function of slope failure probability and the inconvenience of multiple integral calculation, the slope reliability analysis method based on g-line failure domain under the Copula theory is proposed. Firstly, the Copula theory is briefly introduced, and the slope reliability analysis procedure based on Copula theory is given. Then, the g-line curve fitting shape of the general homogeneous slope and the range of shear strength parameters characterizing the failure area of the slope are discussed. The results show that the quadratic polynomial can well fit the g-line curve, and the internal friction angle and cohesion can characterize the failure area under the g-line curve. Taking a homogeneous slope as an example, the failure probabilities of slopes under three kinds of Copula functions are obtained by integrating in the g-line failure area, which are close to the results obtained by the FORM and MCS methods. This proves that under the Copula theory The rationality of slope reliability analysis method based on g - line failure domain. Finally, we discuss the difference of the failure probability calculation results under different Copula functions with the change of safety factor. It is considered that the reliability analysis results are sensitive to Copula function types at low failure probability (high safety factor), and different Copula functions should be emphasized Study on the Variation of Calculation Results Caused by Types and Optimization Problems.